diff --git a/crates/effects/src/distort.rs b/crates/effects/src/distort.rs
index aa72ad2d..8fabb059 100644
--- a/crates/effects/src/distort.rs
+++ b/crates/effects/src/distort.rs
@@ -108,6 +108,10 @@ const MAX_SCALE: f64 = 100_000.0;
 const MAX_MOVE: f64 = 1.0e7;
 /// The Transform effect's copies stop before one reaches further than this (pt) from the origin.
 const MAX_REACH: f64 = 1.0e9;
+/// Most anchors a Transform effect's copies make of a path, the original included: 1000 copies of
+/// a 2000-anchor path. Stacked Transform effects multiply their copies (three of 1000 copies make
+/// a thousand million of one square), so the limit is on the result, not on each effect's count.
+pub(crate) const MAX_COPY_ANCHORS: usize = 2_000_000;
 
 /// Transform effect: scale, rotate and reflect about reference point `reference` of the bounds
 /// (the 9-point grid, 4 = centre), then move; `copies` more times, each from the last. With
@@ -115,6 +119,11 @@ const MAX_REACH: f64 = 1.0e9;
 /// the angle a share of theirs, drawn from `seed` (the object's), so an object keeps its result
 /// on every redraw while each object varies its own way.
 pub fn transform(path: &PathData, b: Rect, p: &Value, seed: u64) -> PathData {
+    transform_within(path, b, p, seed, MAX_COPY_ANCHORS)
+}
+
+/// [`transform`] whose copies make at most `max` anchors of the path, the original included.
+pub(crate) fn transform_within(path: &PathData, b: Rect, p: &Value, seed: u64, max: usize) -> PathData {
     let random = flag(p, "random", false);
     // The share (0..1) of value `k` applied.
     let share = |k: u64| if random { (noise(seed, k, 0, 0) + 1.0) / 2.0 } else { 1.0 };
@@ -132,9 +141,17 @@ pub fn transform(path: &PathData, b: Rect, p: &Value, seed: u64) -> PathData {
         return path.transformed(m);
     }
     let within = |r: Rect| [r.x0, r.y0, r.x1, r.y1].iter().all(|v| v.abs() <= MAX_REACH);
+    // Each copy adds the path once more, and a Transform after this one copies the lot again:
+    // copies stop where the result would pass [`MAX_COPY_ANCHORS`] (#1705).
+    let each = path.anchor_count();
+    let mut anchors = each;
     let mut out = path.clone();
     let mut cur = path.clone();
     for _ in 0..copies {
+        anchors = anchors.saturating_add(each);
+        if anchors > max {
+            break;
+        }
         cur = cur.transformed(m);
         if !cur.bounds().is_some_and(within) {
             break;
diff --git a/crates/effects/src/tests.rs b/crates/effects/src/tests.rs
index ffafc9f8..94430875 100644
--- a/crates/effects/src/tests.rs
+++ b/crates/effects/src/tests.rs
@@ -206,6 +206,24 @@ fn random_transform_is_stable_per_object_and_within_the_values() {
     assert!(close(r.width(), 50.0, 1e-9) && close(r.center().x, 90.0, 1e-9), "{r:?}");
 }
 
+/// #1705: stacked Transform effects multiply their copies; the anchors they make are bounded,
+/// whatever each one's count.
+#[test]
+fn stacked_transform_copies_stay_within_the_anchor_budget() {
+    let p = json!({"copies": 1000});
+    let b = square().bounds().unwrap();
+    let mut path = square();
+    let mut counts = vec![];
+    for _ in 0..3 {
+        path = crate::distort::transform_within(&path, b, &p, 0, 100);
+        counts.push(path.anchor_count());
+    }
+    assert_eq!(counts, [100, 100, 100], "25 squares, then no room for a copy of them");
+    // Within the budget every copy is made, and the effect's own budget takes a thousand copies.
+    assert_eq!(crate::distort::transform_within(&square(), b, &json!({"copies": 24}), 0, 100).subpaths.len(), 25);
+    assert_eq!(run("distort.transform", p, &square()).subpaths.len(), 1001);
+}
+
 #[test]
 fn transform_copies_stop_before_they_overflow() {
     let out = run("distort.transform", json!({"scaleH": 100000, "scaleV": 100000, "copies": 1000}), &square());